A173976 Numbers m such that the concatenation of m and 999 is the lesser of twin primes, i.e., a millennium twin prime couple.

2, 8, 101, 164, 179, 230, 272, 293, 326, 389, 410, 419, 443, 512, 524, 536, 659, 662, 773, 788, 794, 800, 818, 890, 920, 932, 989, 1028, 1058, 1136, 1187, 1238, 1271, 1292, 1310, 1346, 1466, 1490, 1550, 1577, 1583, 1823, 1838, 1856, 1865, 1913, 2003, 2075

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 04 2010

Keywords

• base
• nonn

Comments

Necessarily, m == 2 (mod 3).

Examples

			2 is a term: 2999 = prime(430), 2999+2 = 3001 = prime(431).
8 is a term: 8999 = prime(1117), 8999+2 = 9001 = prime(1118).
		

References

• Richard K. Guy: Unsolved Problems in Number Theory, New York, Springer-Verlag, 1994.
• Theo Kempermann: Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005.
• Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001359, A158277, A158861, A173937.

Programs

Mathematica

tp999Q[n_]:=Module[{c=FromDigits[Join[IntegerDigits[n],{9,9,9}]]}, And @@ PrimeQ[c+{0,2}]]; Select[Range[2500],tp999Q] (* Harvey P. Dale, Oct 03 2013 *)
Select[3 Range[0,700]+2,AllTrue[1000#+{999,1001},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2021 *)

PARI

isok(m) = my(x=eval(Str(m, 999))); isprime(x) && isprime(x+2); \\ Michel Marcus, Mar 08 2023